Fixed point theorems for multi-valued contractions with w-distance

Some fixed point theorems for a few nonlinear multi-valued contraction mappings in complete metric spaces with w-distance are proved. The results presented in this paper generalize the recent results due to Ciric (2009) [3], Feng and Liu (2006) [4], Klim and Wardowski (2007) [8], Latif and Abdou (2011) [12] and Liu et al. (2010) [14]. Seven examples are given to explain our results.

[1]  Dariusz Wardowski,et al.  Fixed point theorems for set-valued contractions in complete metric spaces , 2007 .

[2]  Multivalued generalized nonlinear contractive maps and fixed points , 2011 .

[3]  L. Ciric,et al.  Fixed point theorems for multi-valued contractions in complete metric spaces , 2008 .

[4]  Abdul Latif,et al.  Fixed Points of Generalized Contractive Maps , 2009 .

[5]  Hassen Aydi,et al.  Fixed points for (φ, ψ, p)-weakly contractive mappings in metric spaces with w-distance , 2013, Appl. Math. Comput..

[6]  Abdul Latif,et al.  Fixed Point Results for Generalized Contractive Multimaps in Metric Spaces , 2009 .

[7]  R. F. Brown.  Fixed Point Theory and Its Applications , 1988 .

[8]  I. Altun.  Fixed point and homotopy results for multivalued maps satisfying an implicit relation , 2008 .

[9]  L. Ciric,et al.  Multi-valued nonlinear contraction mappings , 2009 .

[10]  Tayyab Kamran,et al.  Mizoguchi-Takahashi's type fixed point theorem , 2009, Comput. Math. Appl..

[11]  Lai-Jiu Lin,et al.  Some equivalent formulations of the generalized Ekeland’s variational principle and their applications , 2007 .

[12]  Wataru Takahashi,et al.  Fixed point theorems for multivalued mappings on complete metric spaces , 1989 .

[13]  Wataru Takahashi,et al.  Fixed point theorems and characterizations of metric completeness , 1996 .

[14]  Vladimir Rakocevic,et al.  Common fixed points for maps on metric space with w-distance , 2008, Appl. Math. Comput..

[15]  S. Nadler.  Multi-valued contraction mappings. , 1969 .

[16]  Sanyang Liu,et al.  Fixed point theorems for multi-valued contractive mappings and multi-valued Caristi type mappings , 2006 .

[17]  Shin Min Kang,et al.  On Fixed Point Theorems for Multivalued Contractions , 2010 .